6. Laplace Transforms of Integrals


We first saw the following properties in the Table of Laplace Transforms.

1. If G(s) = laplace{g(t)}, then MATH

2. For the general integral, if

MATH

is the value of the integral when t = 0, then:

MATH

EXAMPLES

Use the above information and the Table of Laplace Transforms to find the Laplace transforms of the following integrals:

(a) MATH $dt$

(b) MATH $dt$

(c) MATH $dt$

(d) integral sin at cos at

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